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Topic: Finiteness condition on a morphism of schemes

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finiteness condition on a morphism of schemes

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	Varieties and Schemes for Dummies, Part III \| The String Coffee Table
		Schemes coming from varieties turn out to be in particular integral, seperated and of finite type.
		are equal (known as the ascending chain condition).
		The crucial condition is that it be finitely generated.
	golem.ph.utexas.edu /string/archives/000852.html (1616 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Conditions under which the transitive closure of a well-founded rewrite relation is a well-quasi-rodering are given.
		Also, the class of all the finite structures such that the formula defines a linear order on any of them, is finitely axiomatizable in the class of all finite structures (of the signature).
		This is a part of a larger programme to develop a theory of observable processes where semantics of processes are based on locally and finitely {\em observable\/} process behaviour, and all process constructs are allowed, provided their operational meaning is defined by realistically {\em implementable\/} transition rules.
	www.cs.cmu.edu /Groups/AI/lang/prolog/doc/bib/lics/lics.bib (6365 words)

	Dept. Math/Stats: 2005 Calendar of Events
		Finite sample performances of the MEL estimator and the EL based confidence intervals are evaluated through a simulation study.
		Under certain assumptions, including a nonresonance condition, we proved that smooth linearization is possible in the case of contractions and in a case of saddle.
		However, natural-seeming adaptive schemes often fail to preserve the stationary distribution, thus destroying the fundamental ergodicity properties necessary for MCMC algorithms to be valid.
	www.math.yorku.ca /CalendarOfEvents/2005calendar.html (17623 words)

	[No title]
		An equivalent wsr of expressing the properties (l.8.a) and (l.8.c) is to say that A 0 B (together with the inclusions 22 a,- a 1, b i- 1 0 b) is the coproduct of A and B in the category red of k-reduced algebras, having (k-algebra) homomorphisms as its morphisuis.
		A k-algebra A is finitely generated iff there exists a finite subset (a1,..., a) of A such that each element of A can be expressed as a finite combination of a1,..., a using sums, products, and multiplication by elements of k.
		FINITENESS CONDITIONS We have shown in the previous chapter that any polynomial response map f is realizable by a canonical k-system.
	www.math.rutgers.edu /~sontag/FTP_DIR/polynomial_response_maps.txt (13591 words)

	[No title]
		Up to equivalence, the finite G-CW spectra are those of the form -V 1 B for a finite G-CW complex B and a representation V of G [21, I.8.16].
		Remark 3.6.For finite groups, Theorem 3.2 is a version of [13, 6.5] of tom Dieck and Petrie; for compact Lie groups, it is a version of [10, 1.6] of tom Dieck.
		Under conditions on A specified in [13, 6.* *1], [13, 6.6] proves that A is equivalent to a homotopy representation.
	hopf.math.purdue.edu /Fausk-Lewis-May/FLMApril20.txt (5456 words)

	Calf Abstracts (Site not responding. Last check: 2007-10-29)
		Let V be a representation of a finite group G. Then the symmetric (S) and exterior (L) algebras of V are Koszul dual (over k), in the sense that S \otimes L^* is a bigraded algebra with a natural differential ofdegree (1,-1) which is exact (except in degree (0,0)).
		We ask when a map is a morphism, what is the degree of this morphism, and describe the eventual singularities by looking at the image.
		Actually the theory of schemes is far more general than Algebraic Geometry, and many concepts arising in the geometric context make sense only for a particular kind of schemes usually called "algebraic schemes".
	www.maths.bath.ac.uk /~ntb20/Calf/CalfAbs.html (3933 words)

	[No title]
		These are finite extensions L of Qp, for some Euclidean prime p; the topology defines a natural equivalence class of valuations, with the elements algebraic over Zp * *as (local) valuation ring.
		k finite k} __x be the limit under norms; it is a compactification of W (k)0.
		The former condition [2.166] can be stated as @z~1 = H~0 - [~0, ~1] 12 JACK MORAVA where the grading operator H = (u@u)u=1 is the infinitesimal generator of the Gm -action; it sends uk to kuk.
	hopf.math.purdue.edu /Morava/Rosendal.txt (6109 words)

	[No title]
		The functional dual induces an equivalence of the category of finite dimensional k-vector spaces with its own opposite, but it does not extend to an equivalence on the whole category of k-vector spaces.
		The importance of finite complexes is no surprise since we are defining homotopy theories that work well with respect to Spanier-Whitehead duality.
		For condition (3), note that ssk colimtF (X", S0) is isomorphic to colim tss-k Xt (and similarly for "Y).
	jdc.math.uwo.ca /papers/duality.txt (7642 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Now the lemma follows from the fact that if $G$ is a finite abelian group with an alternating nondegenerate pairing, then there is a finite abelian group~$H$ such that $G \ncisom H \times H$ as groups (e.g., see~\cite[Prop.~2]{delaunay}).
		This extended morphism $j: {\calC}_{/X_p} \to {\tilde F}[p]_{X_p}$ is necessarily a closed immersion since ${\calC}_{/X_p}$ is a multiplicative type finite flat group scheme.
		However, the cokernel of this morphism restricted to the fiber in characteristic~$3$ is, in both of these cases, a cyclic group with nontrivial $G_{\bf Q_3}$-action and hence is $3$-cohomologically trivial.
	modular.math.washington.edu /papers/shacomp/shacomp_v13 (9029 words)

	[No title]
		In this case one uses coverings by affine schemes, which are acyclic for coherent sheaf cohomology by a classical theorem of Serre.
		U}, there is a finite subset {Ui1; :::; Uin} which is also a cover* ing 32 family.7 For example, if X is a noetherian scheme* then theetale, Nisnevich and Zariski sites of X are noetherian (although in the case of the Nisnevich site this isn't obvious - see [44], appendix E, 6a).
		If W is not finite then some condition has to be imposed on the site, the object, the presheaf or all three.
	www.math.purdue.edu /research/atopology/Mitchell/thomason.txt (10189 words)

	Atlas: Joint Meeting of AMS, DMV, and ÖMG - Abstracts (Site not responding. Last check: 2007-10-29)
		Let G be a split extension of a finitely generated free group F by a torsion free hyperbolic group H. Then the conjugacy problem in G is solvable iff the canonical image of H in Aut(F) is orbit decidable.
		We shall describe a practical computer method for calculating the integral cohomology of a finite group G. The method is based on the notion of a "homotopical syzygy" and involves the construction of a reasonably small CW-space X on which G acts freely.
		In the theory of finite groups it is well known that local properties, such as those of p-subgroups and their normalizers, influence the global structure of the groups.
	atlas-conferences.com /cgi-bin/abstract/select/caoz-01?session=x (14424 words)

	mathBlog » arXiv (Site not responding. Last check: 2007-10-29)
		A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A isa noncommutative quasi-coherent O_X-ring.
		For a separateddifferential quasi-coherent ringed scheme of finite type over a field, we proveexistence and uniqueness of a rigid dualizing complex.
		Montgomery and S. Witherspoon proved that upper and lower semisolvable,semisimple, finite dimensional Hopf algebras are of Froebenius type when theirdimensions are not divisible by the characteristic of the base field.
	www.ibiblio.org /litlfred/mathBlog/category/arxiv (2829 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		For a subscheme $\fY$ of $\fX$ the formal neighborhood $FN_\fX(\fY)$ is an ind-scheme (a formal scheme), the notation for the corresponding categories of modules is introduced in \ref{Derived categories of sheaves supported on a subscheme}, \ref{Categories} and \ref{Categories with chi}.
		The Frobenius map of schemes $X \ra X $ is defined as identity on topological spaces, but the pull-back of functions is the $p$-th power:\ $\Frx^*(f)= f^p$ for $f\in \OO_{X\tw}= \OO_X$.
		The adjunction morphism viewed as $M\to \pl_W\ M$, equals $\sum _W id_M$ (when $M$ is the restriction of $U$ to the $n\thh$ infinitesimal neighborhood of $\la$ this follows by restricting $\tii U\con \R\Ga(\tii\DD)$).
	www.math.northwestern.edu /~bezrukav/30 (10229 words)

	schedule.html
		closure of a scheme as a scheme instead of as a quasi-coherent algebra.
		to $\frak{m}$ is finitely generated for all integers $i \ne d$.
		Abstract: Let R be a local ring and M a finitely generated R-module.
	dreadnought.uta.edu /~dave/schedule.html (3068 words)

	Osaka Journal of Mathematics (Site not responding. Last check: 2007-10-29)
		Zhu, L. : The generic finiteness of the M-canonical map for 3-folds of general type.
		Geck, M. : The Schur indices of the cuspidal unipotent characters of the finite chevalley groups E7(q).
		Kuroda, S. : A finite universal SAGBI basis for the kernel of a derivation.
	www.math.sci.osaka-u.ac.jp /ojm/contents.html (5282 words)

	[No title]
		We're on the verge of being able to define an affine scheme.
		By the proof of quasicompactness, this means that we have a (finite partition of unity) relation of the form
		Since that map is injective, the second condition reduces to the statement that
	odin.mdacc.tmc.edu /~krc/agathos/schem.html (1113 words)

	[No title]
		Or, the dichotomy condition could be strengthened to "For all a,b there exists c such that either a ~ b+c or b ~ a+c.") Proof: Given b in FinC, use dichotomy to shed its n elements sequentially yielding b = 0+1+...+1.
		Since the concept of "finite set" is sitting right in the definition of FinC, we have to know all about finite sets to use this characterization of FinSet...
		In particular you see there discussed Kuratowski finiteness (you can list of all the elements but can't necessarily remove duplicates), finite decidable (in addition you can detect inequality between elements and so can remove duplicates) and finite ordinals (there is a canonical list that thereby puts an ordering on the elements).
	www.mta.ca /~cat-dist/archive/2001/01-11 (16205 words)

	[No title]
		However, experience sug* gests that such theorems require finiteness* conditions which are not satisfied in the category * *of spectra.
		The Hopkins-Gross theorem is a ki* *nd of analog of Serre duality in the K(n)-local stable homotopy category.
		The set E0W is finite by an easy thick subcategory argument [12, Theorem 8.5] so the st* abiliser of u has finite* index in.
	www.math.purdue.edu /research/atopology/Strickland/st-ghd.txt (4246 words)

	Appendix: Some Facts Concerning Toric Reduction (Site not responding. Last check: 2007-10-29)
		Cartier duality interchanges étaleness and multiplicativeness, as well as closed immersions and faithfully flat maps (as the latter two properties may be checked on the closed fiber, for which one is reduced to the standard case of finite commutative group schemes over a field).
		Since faithful flatness is equivalent to surjectivity (for maps between étale schemes over a base), the lemma is now physically clear.
		The second part, concerning group schemes, is a mechanical consequence of the first part (including the functoriality of the finite part).
	modular.fas.harvard.edu /papers/compgrp/compgrp/node20.html (1436 words)

	by E Cartan;
		Kinetic Schemes for Solving Saint坊enant Equations on Unstructured Grids (M O Bristeau and B Perthame)
		Conditional Grammars with Restrictions by Syntactic Parameters (J Dassow)
		Iterated Morphisms with Complementarity on the DNA Alphabet (A Salomaa)
	www.yurinsha.com /341/p9.htm (942 words)

	Previous Rutgers Algebra Seminars (Since 1995)
		We first give an equivalent form of the ``compatibility condition,'' one of the important tools in the theory of Huang and Lepowsky, in terms of a ``strong lower truncation condition.'' We use this to establish the equivalence of the two tensor product functors constructed in the two totally different approaches.
		By introducing Frobenius-Lie morphism, a connection between finite-dimensional representations of finite Lie algebras over finite fields and their algebraic closures is established, which enables us to understand irreducible representations of classical Lie algebras over a finite field $F_q$ through the ones of its extension over $\bar F_q$.
		The scheme is then extended in the wider context of the corresponding `coloured' counterparts.
	www.math.rutgers.edu /~weibel/oldalgebra.sem.html (8477 words)

	some bibliography: B
		The properties of such a bracket are related to the properties of the finite dimensional algebra with structure constants $b\sb k\sp{ij}$.
		Abstract: It is known that a finite group with just two different sizes of conjugacy classes must be nilpotent and it has recently been shown that its nilpotence class is at most 3.
		We show that the morphism which compares their Hochschild cohomology algebras is a Gerstenhaber algebras morphism.
	www.justpasha.org /math/bib/b.html (8846 words)

	some bibliography: S
		We apply this generalization to complex spaces and noetherian schemes and deduce two decomposition theorems for their (relative) Hochschild cohomology (special cases of those were recently shown by Buchweitz-Flenner and Yekutieli).
		A crucial new ingredient is the concept of a regular neighbourhood for a finite family of almost invariant subsets of a group.
		Similarly, rather mild conditions on a ${\germ g}\text{-module}$ force it to be isomorphic to a ${\germ g} \text{-module}$ of a very simple kind, called a Kaplansky module $V$ ($V$ depends on two real parameters).
	www.justpasha.org /math/bib/s.html (7790 words)

	Morel, Voevodsky: $A^1$-homotopy theory of schemes
		DIEUDONNÉ, Étude locale des schémas et des morphismes de schémas (EGA 4), Publ.
		NISNEVICH, The completely decomposed topology on schemes and associated descent spectral sequences in algebraic K-theory.
		TROBAUGH, Higher algebraic K-theory of schemes and of derived categories, In The Grothendieck festchrift, vol.
	www.numdam.org /numdam-bin/recherche?h=nc&id=PMIHES_1999__90__45_0&format=complete (259 words)

	Search Results for Riemann
		It gives necessary and sufficient conditions for the triangulability of topological surfaces and in proving these results he completed work on a problem which had been studied by some of the most famous of mathematicians Riemann, Poincare, and Weyl.
		Hooley has proved it under the condition that a strong form of Riemann's hypothesis (for number fields) is valid.
		By removing a finiteness condition which is habitually made on the angles formed by the various elements of a pencil (of lines, planes, etc.), Sommerville obtained more general geometries than the usual ones (Euclid, Lobachevsky, Riemann).
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Riemann&CONTEXT=1 (9102 words)

	Errata for Course Notes
		Then #D_n = 2n for all n and the (finite) dihedral groups are precisely the groups generated by two elements of order 2.
		In more detail, let H be the subgroup of G consisting of the elements almost all of whose components are zero (an infinite countable direct sum of copies of the cyclic group of order 2).
		The inverse image in G of the subspace of G/H spanned by the basis with a finite number of elements omitted will be a subgroup of finite index in G whose closure is G. p143.
	www.jmilne.org /math/CourseNotes/errata.html (6178 words)

	Hartshorne: On the de Rham cohomology of algebraic varieties
		FRISCH, Points de platitude d'un morphisme d'espaces analytiques complexes, Inv.
		GROTHENDIECK, Crystals and the De Rham cohomology of schemes (Notes by I. COATES and O. JUSSILA) in Dix exposés sur la cohomologie des schémas, North-Holland,
		LIEBERMAN, Duality and the De Rham cohomology of infinitesimal neighborhoods, Invent.
	math-doc.ujf-grenoble.fr /numdam-bin/item?id=PMIHES_1975__45__5_0 (552 words)

	Köck: The Grothendieck-Riemann-Roch theorem for group scheme actions
		ATIYAH, Characters and cohomology of finite groups (Publ.
		TAYLOR, Riemann-Roch type theorems for arithmetic schemes with a finite group action (J. Reine Angew.
		THOMAS, Characteristic classes and the cohomology of finite groups (Cambridge Stud.
	math-doc.ujf-grenoble.fr /numdam-bin/item?id=ASENS_1998_4_31_3_415_0 (560 words)

	Papers
		On the finiteness of rational curves on quintic threefolds
		The multiple-point schemes of a finite curvilinear map of codimension one
		A new explicit finite free resolution of ideals generated by monomials in an R-sequence
	www.math.fsu.edu /~aluffi/mainhtmls/compr.html (6252 words)

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